Optical communications systems typically include a pair of network nodes connected by an optical waveguide (i.e., fiber) link. Within each network node, communications signals are converted into electrical signals for signal regeneration and/or routing, and converted into optical signals for transmission through an optical link to another node. The optical link between the network nodes is typically made up of multiple concatenated optical components, including one or more (and possibly 20 or more) optical fiber spans (e.g., of 40-150 km in length) interconnected by optical amplifiers.
In modern optical communications networks, it is generally desirable to transmit optical signals at high power levels in order to maintain sufficient signal to noise ratios over extended transmission distances, and thereby obtain an acceptably low Bit Error Rate (BER) in a received optical signal. However, conventional optical fibres comprise an optical transmission medium which exhibits nonlinear effects at high optical power levels, resulting in degradation of the optical signal. These nonlinear effects are generally a function of optical power, and so any increase in transmission power level tends to increase signal degradations due to system nonlinearities. Nonlinear effects may similarly occur within optical terminals of the system, in optical transmission media or in components such as optical amplifiers. The optimum power level at which optical signals can be transmitted is typically the maximum power level at which significant degradation due to nonlinearity is avoided. Since the performance of various optical components within the system varies with operating conditions, age, and component replacement, a safety margin is used in setting the maximum power level. Consequently, optical communications systems typically operate at power levels which are less than the optimum power level. A detailed discussion of nonlinear optical effects is provided by Agrawal, Govind P., “Nonlinear Fiber Optics”, 2nd. Ed., Academic Press, Inc., San Diego, Calif., 1995 (ISBN 0-12-045142-5).
Of particular concern in considering nonlinear processes are the effects of phase nonlinearities, which increase as data rates and optical power levels increase, and which ultimately limit both system performance and signal reach.
Phase nonlinearities are the result of complex interactions between the optical power present in the fiber, the refractive index of the fiber medium, the wavelength-division-multiplexing (WDM) channel spacing, the polarization states of the signals within each of the channels, and the proximity of channel wavelengths to the zero-dispersion wavelength of the fiber. Phase nonlinearities include self-phase modulation (SPM), cross-phase modulation (XPM), and modulation-instability (MI), all of which are discussed in detail in Agrawal (supra), at chapters 4 and 7.
As shown in FIG. 1a, a conventional optical communications system may conveniently be represented by a transmitter 2 and a receiver 6 separated by an optical link 4. As is well known in the art, the link 4 may include multiple optical fiber spans separated by active optical devices such as, for example, optical amplifiers, channel equalizers etc. For simplicity of illustration, these elements are not shown in the drawings. Signal distortions due to non-linear effects, including Self Phase Modulation (SPM), cross-phase modulation (XPM), Modulation instability (MI) and four-wave mixing impressed on optical signals traversing the link 4 are represented (that is, approximated) by a link complex nonlinear operator T[E(t)]; where T[ ] is the operator, and E(t) is any optical signal. Known methods such as Voltarra Series can be used to represent the link operator T[E(t)]. See, for Example, Voltarra and Wiener, “theories of Non-Linear Systems”, Martin & Schetzen, John Wiley & Sons., 1980. This link operator T[E(t)]t can be derived using known methods, such as, for example, as discussed in detail in Agrawal (supra). T[E(t)] can encompass one-to-one non-linear effects, in which an optical signal in one channel suffers distortions due to itself; many-to-one non-linear effects, in which an optical signal in one channel suffers distortions due to optical signals in two or more channels; and many-to-many non-linear effects, in which optical signals in many channels suffer distortions due to optical signals in many channels. For the sake of simplicity, the present invention is described by reference to embodiments that concentrate on compensation of one-to-one non-linear effects, it being understood that the same principles may be applied to many-to-one and many-to-many non-linear effects, without departing from the scope of the present invention. Linear Cross-talk is an artefact of the finite bandwidth of channel filters used to demultiplex closely spaced channels of a WDM signal arriving at the receiver 6 through the link 4. This finite bandwidth results in some optical signal power in one channel “leaking” through the filters of adjacent channels. Non-linear cross-talk occurs through mechanisms such as 4-wave mixing and XPM, as discussed in detail in Agrawal (supra).
In operation, a communication signal (or bit-stream) in the form of an electrical input signal x(t) 8 is converted into a corresponding optical signal EIN(t) 10 by a conventional Electrical-to-Optical (E/O) converter 12. The optical signal EIN(t) is then multiplexed into a WDM signal 14 by a conventional channel multiplexer 16. As the WDM signal 14 traverses the optical link 4, it is distorted by the complex nonlinear link operator T[ ], and arrives at the receiver 6 as adistorted WDM signal 14a. Within the receiver 6, a received optical channel signal EOUT(t)[=T[EIN(t)]] 18 is demultiplexed from the distorted WDM signal 14a by a conventional demultiplexer 20 and converted into a corresponding electrical output signal y(t) 22 by a conventional Optical-to-Electrical (O/E) converter 24.
Various methods have been proposed for compensating non-linearities within an optical communications system. These systems typically operate by inserting one or more compensators within the link 4, represented in FIG. 1b by the compensation operator C[E(t)], where C[ ] is the operator and E(t) is any input optical signal. The compensation operator C[E(t)] is selected to optimize performance of the link 4. Ideally, the compensation operator C[E(t)] is equivalent to the inverse of the link operator T[E(t)], in which case T[C[E(t)]]=E(t), and the combined effect of T[ ] and C[ ] would be an undistorted received signal EOUT(t)=T[C[EIN(t)]] that exactly corresponds to the original optical signal EIN(t).
For example, co-assigned U.S. Pat. No. 6,124,960, entitled Transmission System with Cross-Phase Modulation Compensation, which issued on Sep. 26, 2000, describes a WDM transmission system carrying amplitude modulated traffic in which significant cross-phase modulation occurs. In this case, the compensation operator C[E(t)] is provided by “pre-chirping” each of the individual optical channels at the transmitter (that is, upstream of the channel MUX) with replicas, or low-pass filtered replicas of the amplitude modulation applied to each of the other channels. Pre-chirping of a channel in this manner imposes a chirp (or frequency shift) that is approximately equal and opposite to the XPM-induced chirp of the fiber link. Pre-chirping of each individual channel with a replica of the amplitude modulation applied to that same channel may also be used in order to provide compensation for self-phase modulation (SPM).
A limitation of this technique is that the pre-chirp is imposed as a discrete step prior to MUXing each channel into the optical fiber link 4. However, within the link 4, XPM (and SPM) induced chirp, and the associated time-domain signal distortions are distributed effects, in that they are a function of dispersion and link length. Consequently, while this technique facilitates compensation of XPM and SPM-induced frequency-domain signal distortions, it is not capable of fully compensating the associated time-domain distortions.
In co-assigned U.S. Pat. No. 6,067,180, entitled Equalization, Pulse Shaping and Regeneration of Optical Signals, which issued on May 23, 2000, the compensation operator C[E(t)] is provided by optical modulators that can be used at the receiver 6 to remove optical distortions (including SPM and XPM) from an inbound optical signal. A limitation of this approach is that the optical modulators tend to be complex, and thus expensive, and suffer high insertion losses. This latter issue reduces the desirability of these modulators in long-haul optical network links, in which the optical signal arriving at the receiver already have a low signal-to-noise ratio.
A technique for fully compensating effects of chromatic dispersion (including SPM) is described in “Exact Compensation for Both Chromatic Dispersion and Kerr Effect in a Transmission Fiber Using Optical Phase Conjugation” (Watanabe, S., et al., Journal of Lightwave Technology, Vol. 14, No. 3, March 1996, pp 243-248). In this technique, the optical fiber link is divided into two fiber sections separated by an Optical Phase Conjugator. The first section is designed as a highly dispersive medium, in which the dispersion is designed to mirror that of the second section. As a result, signal distortions impressed on an optical signal propagating through the first section will be offset by those of the second section. In effect, the compensation operator C[E(t)] is provided by the dispersion profile of the first section, and the optical phase conjugator. Theoretically, if the dispersion profile of the first section can be made to exactly mirror that of the second section, then the compensation operator C[E(t)] will be the inverse of the non-linear operator T[ ], and a substantially undistorted signal EOUT(t)≈EIN(t) will appear at the receiver-end of the optical fiber link.
This technique suffers numerous disadvantages. In particular, the first span must be designed so that the dispersion profile (along the length of the first section) closely mirrors the dispersion profile of the second section. This means that the first section must be uniquely designed for its corresponding second span, which dramatically increases costs. Furthermore, known optical phase conjugators are expensive, attenuate the optical signal, and introduce noise. Theoretically, the optical phase conjugator may be eliminated by designing the first section such that both the power and dispersion profiles of the first section mirror those of the second section. However, this solution is extremely difficult to implement in the optical domain, because mirroring of the power profile of the second section requires that the first section be provided with fiber spans with gain, and amplifiers with loss.
Accordingly, a cost-effective technique for mitigating the signal distortions due to non-linear effects in a WDM optical communications system remains highly desirable.